DLASQ1(3)      LAPACK routine of NEC Numeric Library Collection      DLASQ1(3)



NAME
       DLASQ1

SYNOPSIS
       SUBROUTINE DLASQ1 (N, D, E, WORK, INFO)



PURPOSE
            DLASQ1 computes the singular values of a real N-by-N bidiagonal
            matrix with diagonal D and off-diagonal E. The singular values
            are computed to high relative accuracy, in the absence of
            denormalization, underflow and overflow. The algorithm was first
            presented in

            "Accurate singular values and differential qd algorithms" by K. V.
            Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,
            1994,

            and the present implementation is described in "An implementation of
            the dqds Algorithm (Positive Case)", LAPACK Working Note.




ARGUMENTS
           N         (input)
                     N is INTEGER
                   The number of rows and columns in the matrix. N >= 0.

           D         (input/output)
                     D is DOUBLE PRECISION array, dimension (N)
                   On entry, D contains the diagonal elements of the
                   bidiagonal matrix whose SVD is desired. On normal exit,
                   D contains the singular values in decreasing order.

           E         (input/output)
                     E is DOUBLE PRECISION array, dimension (N)
                   On entry, elements E(1:N-1) contain the off-diagonal elements
                   of the bidiagonal matrix whose SVD is desired.
                   On exit, E is overwritten.

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension (4*N)

           INFO      (output)
                     INFO is INTEGER
                   = 0: successful exit
                   < 0: if INFO = -i, the i-th argument had an illegal value
                   > 0: the algorithm failed
                        = 1, a split was marked by a positive value in E
                        = 2, current block of Z not diagonalized after 100*N
                             iterations (in inner while loop)  On exit D and E
                             represent a matrix with the same singular values
                             which the calling subroutine could use to finish the
                             computation, or even feed back into DLASQ1
                        = 3, termination criterion of outer while loop not met
                             (program created more than N unreduced blocks)



LAPACK routine                  31 October 2017                      DLASQ1(3)